There are many ways of answer this question. I view God as a programmer. He created the laws of physics and upon execution, our universe popped out and began developing. Chief of these algorithms is the law of Cause and Effect. Also known as Karma, the law of Cause and Effect underpins everything in the universe. Without it, we could not exist. We are the direct effect of stars exploding to create the atoms that compose our bodies.
So what does Karma have to do with suffering? We are viewing the question from the wrong angle. God doesn’t allow suffering. It simply is. It is a result of His loving programming. The vast majority of Causes and Effects are beautiful and good. Even a devastating flood causes benefit further down the chain. It can bring good soil or clear land for new habitat.
Even the ultimate human suffering, death, is good. It makes room for new people to live. It creates a history of knowledge and experience that remains unbroken. It pulls families closer. It teaches those living to truly live. It finally brings us home to God. I’d say those are good things!
Karma underlies everything, even God. God caused everything; he also has the effect of having something to love. Likewise that love caused Him to create everything. It is a closed cycle.
So why does God allow Suffering? Because all things must suffer to exist. Even God suffers. He suffers when we suffer or when a star snuffs out a planet. He also rejoices when a new life, a new solar system, or a new galaxy is born.
This question is too small when you think about it. In the grand vast panorama of the universe, suffering is small compared to the vast continuing creation seen every moment. It is small in the beauty Cause and Effect creates. Every human life is the size of a neutrino in the scope of the universe. However, every neutrino is important to the fabric of the universe.